Once one of the most prominent Republican lobbyists in the capital, known for flying congressmen to global junkets on a private jet, his spectacular downfall led to a three-and-a-half year stint in federal prison where he wasn't even allowed to hold enough change in his pocket to operate the vending machines.

Now he's back, having reinvented himself as a critic of the Washington lobbying industry he once dominated and as a speaker and radio show host. He calls much of the lobbying industry "legalized bribery" and gives advice on the temptations of corruption.

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Former US lobbyist Jack Abramoff

So you might think Abramoff would have some interesting things to say about the incoming Trump administration, and he does.

For one, despite his new efforts as a reformer, Abramoff doesn't think Trump should be forced to release his tax returns.

"I don't know that it matters," Abramoff said in an interview with CNBC. "I think most Americans basically say, 'On one hand, we get to see Donald Trump's tax returns. On the other hand, we get to try to return the country to what it should be. I'll go with returning the country to what it should be. I don't care what's in his tax returns.'"

Abramoff also said he understands Trump's desire for privacy, given that Abramoff's own scandal involved the release of thousands of private email messages and the damaging fallout from those private conversations.

Abramoff doesn't think Trump will divest himself from the Trump Organization conglomerate that made him a billionaire. "He'll figure out what are the laws, what exactly is legal and not legal, and he'll do that and not care about the optics because, guess what, for the last year and a half he's not cared about optics and he got elected president," Abramoff said.

But Abramoff said that Republicans on Capitol Hill missed the message of the 2016 election this week when they took initial steps to weaken the independent Office of Congressional Ethics, before reversing themselves on Tuesday.

"The election of November was about reforming Washington, probably more even than when Obama ran in 2008," Abramoff said. "People are sick and tired of the way things are happening here, and they elected the ultimate outsider in Donald Trump. And as a consequence, they don't want to see Congress behave like this."